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Introductory Microeconomics (ES10001). Topic 3: Production and Costs. I. Introduction. We now begin to look behind the Supply Curve Recall: Supply curve tells us: Quantity sellers willing to supply at particular price per unit;

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Introductory microeconomics es10001

Introductory Microeconomics (ES10001)

Topic 3: Production and Costs


I introduction
I. Introduction

  • We now begin to look behind the Supply Curve

  • Recall: Supply curve tells us:

    • Quantity sellers willing to supply at particular price per unit;

    • Minimum price per unit sellers willing to sell particular quantity

  • Assumed to be upward sloping


  • I introduction1
    I. Introduction

    • We assume sellers are owner-managed firms (i.e. no agency issues)

    • Firms objective is to maximise profits

    • Thus, supply decision must reflect profit-maximising considerations

    • Thus to understand supply decision, we need to understand profit and profit maximisation


    Figure 1: Optimal Output

    q*

    Costs of Production

    Revenue

    ‘Optimal’ Output


    Ii profit
    II. Profit

    • Profit = Total Revenue (TR) - Total Costs (TC)

    • Note the important distinction between Economic Profit and Accounting Profit

    • Opportunity Cost (OC) - amount lost by not using a particular resource in its next best alternative use.

    • Accountants ignore OC - only measure monetary costs


    Ii profit1
    II. Profit

    • Example: self-employed builder earns £10 and incurs £3 costs; his accounting profit is thus £7

    • But if he had the alternative of working in MacDonalds for £8, then self-employment ‘costs’ him £1 per period.

    • Thus, it would irrational for him to continue working as a builder


    Ii profit2
    II. Profit

    • Formally, we define accounting profit as:

    • where TCa = totalaccountingcosts. We define economic profit as:

    • where TC = TCa + OC denotes total costs


    Ii profit3
    II. Profit

    • Thus:

    • Thus, economists include OC in their (stricter) definition of profits


    Ii profit4
    II. Profit

    • Define Normal (Economic) Profit

    • That is, where accounting profit just covers OC such that the firm is doing just as well as its next best alternative.


    Ii profit5
    II. Profit

    • Define Super-normal (Economic) Profit:

    • Supernormal profit thus provides true economic indicator of how well owners are doing by tying their money up in the business


    Iii the production decision
    III. The Production Decision

    • Optimal (i.e. profit-maximising) q (i.e. q*) depends on marginal revenue (MR) and marginal cost (MC)

    • Define: MR = ΔTR / Δq

      MR = ΔTC / Δq

    • Decision to produce additional (i.e. marginal) unit of q (i.e. Δq = 1) depends on how this unit impacts upon firm’s total revenue and total costs


    Iii the production decision1
    III. The Production Decision

    • If additional unit of qcontributes more to TR than TC, then the firm increase production by one unit of q

    • If additional unit of qcontributes less to TR than TC, then the firm decreases production by one unit of q

    • Optimal (i.e. profit maximising) q (i.e. q*) is where additional unit ofq changesTR and TC by the same amount


    Iii the production decision2
    III. The Production Decision

    • Strategy:

      • MR > MC=>Increase q

      • MR < MC=>Decrease q

      • MR = MC=>Optimal q (i.e. q*)

  • Thus, two key factors:

    • Costs firm incurs in producing q

    • Revenue firm earns from producing q

  • We will look at each of these factors in turn.


  • Iii the production decision3
    III. The Production Decision

    • Revenue affected by factors external to the firm. essentially, the environment within which it operates

    • Is it the only seller of a particular good, or is it one of many? Does it face a single rival?

    • We will explore the environments of perfect competition, monopoly and imperfect competition

    • But first, we explore costs


    Iv costs
    IV. Costs

    • If the firm wishes to maximise profits, then it will also wish to minimise costs.

    • Two key factors determine costs of production:

      • Cost of productive inputs

      • Productive efficiency of firm

  • i.e. how much firm pays for its inputs; and the efficiency with which it transforms these inputs into outputs.


  • Iv costs1
    IV. Costs

    • Formally, we envisage the firm as a production function:

      q = f(K, L)

    • Firm employs inputs of, e.g., capital (K) and labour (L) to produce output (q)

    • Assume cost per unit of capital is r and cost per unit of labour is w


    Figure 2: The Firm as a Production Function

    smoke

    r

    K

    q = f(K, L)

    L

    w

    Inputs Output


    Iv costs2
    IV. Costs

    • Assume for simplicity that the unit cost of inputs are exogenous to the firm

    • Thus, it can employ as many units of K and L it wishes at a constant price per unit

    • To be sure, if w = £5, then one unit of L would cost £5 and 6 units of L would cost £30

    • Consider, then, productive efficiency


    V productive efficiency
    V. Productive Efficiency

    • We describe efficiency of the firm’s productive relationship in two ways depending on the time scale involved:

      • Long Run: Period of time over which firm can change all of its factor inputs

      • Short Run: Period of time over which at least one of its factor is fixed.

  • We describe productive efficiency in:

    • Long Run: ‘Returns to Scale’

    • Short Run: ‘Returns to a Factor’


  • Vi returns to scale
    VI. Returns to Scale

    • Describes the effect on q when all inputs are changed proportionately

    • e.g. double (K, L); triple (K, L); increase (K, L), by factor of 1.7888452

    • Does not matter how much we increase capital and labour as long as we increase them in the same proportion


    Vi returns to scale1
    VI. Returns to Scale

    • Increasing Returns to Scale: Equi-proportionate increase in all inputs leads to a more than equi-proportionate increase in q

    • Decreasing Returns to Scale: Equi-proportionate increase in all inputs leads to a less than equi-proportionate increase in q

    • Constant Returns to Scale: Equi-proportionate increase in all inputs leads to same equi-proportionate increase in q


    Vi returns to scale2
    VI. Returns to Scale

    • What causes changes in returns to scale?

    • Economies of Scale: Indivisibilities; specialisation; large Scale / better machinery

    • Diseconomies of Scale: Managerial diseconomies of Scale; geographical diseconomies

    • Balance of two forces is an empirical phenomenon (see Begg et al, pp. 111-113)


    Vi returns to scale3
    VI. Returns to Scale

    • How do returns to scale relate to firm’s long run costs?

    • Efficiency with which firm can transform inputs into output in the long run will affect the cost of producing output in the long run

    • And this, will affect the shape of the firms long run total cost curve


    Figure 3: LTC & Constant Returns to Scale

    c

    LTC

    15

    10

    5

    q

    0

    10 20 30




    Vi returns to scale4
    VI. Returns to Scale

    • LTC tells firm much profit is being made given TR; but firm wants to know how much to produce for maximum profit.

    • For this it needs to know MR and MC

    • So can LTC tell us anything about LMC?

    • Yes!


    Vi returns to scale5
    VI. Returns to Scale

    • Slope of line drawn tangent to LTC curve at particular level of q gives LMC of producing that level of q

    • i.e.


    Figure 6a: LTC & LMC

    c

    LTC

    x

    q

    0

    q0q1

    Tan x = LTC / q


    Figure 6b: LTC & LMC

    c

    LTC

    x

    q

    0

    q0q1

    Tan x = LTC / q


    Figure 6c: LTC & LMC

    c

    LTC

    x

    q

    0

    q0q1

    Tan x = LTC / q


    Figure 6d: LTC & LMC

    c

    LTC

    x

    q

    0

    q0

    Tan x = LMC(q0)




    Vi returns to scale6
    VI. Returns to Scale

    • Similarly, slope of line drawn from origin to point on LTC curve at particular level of q gives LAC of producing that level of q

    • i.e.


    Figure 8: LTC & LAC

    c

    LTC

    x

    q

    0

    q0

    Tan x = LAC(q0)


    Figure 9: IRS Implies Decreasing LAC

    c

    LTC

    x

    z

    q

    0

    Tan x = LAC(q0)



    Vi returns to scale7
    VI. Returns to Scale

    • Generally, we will assume that firms first enjoy increasing returns to scale (IRS) and then decreasing returns to scale (DRS)

    • Thus, there is an implied ‘efficient’ size of a firm

    • i.e. when it has exhausted all its IRS

    • qmes - ‘minimum efficient scale’



    Vi returns to scale8
    VI. Returns to Scale

    • Note the relationship between LMC and LAC:

      q < qmes LMC < LAC

      q = qmes LMC = LAC

      q > qmes LMC > LAC


    Figure 12a: IRS and then DRS

    c

    LTC

    LMC < LAC

    q

    0


    Figure 12b: IRS and then DRS

    c

    LTC

    LAC =LMC

    LMC < LAC

    q

    0


    Figure 12c: IRS and then DRS

    c

    LTC

    LMC > LAC

    LAC =LMC

    LMC < LAC

    q

    0


    Figure 12d: IRS and then DRS

    c

    LTC

    LMC > LAC

    LAC =LMC

    LAC > LMC

    q

    0

    qmes


    Vi returns to scale9
    VI. Returns to Scale

    • Thus:

      LAC is falling if: LMC < LAC

      LAC is flat if: LMC = LAC

      LAC is rising if: LMC > LAC


    Figure 13: IRS Implies Decreasing LAC

    c

    LTC

    0

    q

    LMC

    LAC

    q

    0

    qmes


    Vii returns to a factor
    VII. Returns to a Factor

    • Returns to a factor describe productive efficiency in the short run when at least one factor is fixed

    • Usually assumed to be capital

    • Short-run production function:


    Vii returns to a factor1
    VII. Returns to a Factor

    • Increasing Returns to a Factor: Increase in variable factor leads to a more than proportionate increase in q

    • Decreasing Returns to a Factor: Increase in variable factor leads to a less than proportionate increase in q

    • Constant Returns to a Factor: Increase in variable factor leads to same proportionate increase in q


    Figure 14: Returns to a Factor

    q

    IRF

    CRF

    DRF

    L

    0

    Short-Run Production Function:


    Vii returns to a factor2
    VII. Returns to a Factor

    • Implications for short-run total cost curve

    • Constant returns to a factor implies we can double q by doubling L; if unit price of L is constant, this implies a doubling of cost

    • Similarly, if returns to a factor are increasing (i.e. less than doubling of costs) or decreasing (more than doubling of costs)


    Figure 15: Returns to a Factor

    c

    SRTCDRF

    SRTCCRF

    SRTCIRF

    TFC

    q

    0


    Vii returns to a factor3
    VII. Returns to a Factor

    • Fixed and Variable Costs

    • Since in the short run at least one factor is fixed, the costs associated with that factor will also be fixed and so will not vary with output

    • Thus, in the short run, costs are either:

      • Fixed: Do not vary with q (e.g. rent)

      • Variable: Vary with q (e.g. energy, wages)



    Vii returns to a factor5
    VII. Returns to a Factor

    • The ‘Law of Diminishing Returns’

    • Whatever we assume about the returns to scale characteristics of a production function, it is always that case that decreasing returns to a factor (i.e. diminishing returns) will eventually set in

    • Intuitively, it becomes increasingly difficult to raise q by adding increasing quantities of a variable input (e.g. L) to a fixed quantity of the other input (e.g. K)


    Figure 16: Returns to a Factor

    c

    STC

    STVC

    SFC

    q

    0


    Figure 17: Returns to a Factor

    c

    SMC

    SAC

    SAVC

    SAFC

    q

    0


    Viii long short run costs
    VIII. Long- & Short-Run Costs

    • What is the relationship between long-run and short-run costs?

    • The latter are derived for a particular level of the fixed input (i.e. capital)

    • We can examine the relationship via the tools we developed in our study of consumer theory


    Viii long short run costs1
    VIII. Long- & Short-Run Costs

    • We envisage the firm as choosing to maximise its output subject to a cost constraint

    • or:

    • Minimising its costs subject to an output constraint

    • N.B. Assumption of competitive markets


    Viii long short run costs2
    VIII. Long- & Short-Run Costs

    • Formally:

    • Max q = f(K, L) s.t c = wL + rK = c0

    • or:

    • Min c = wL + rK s.t q = f(K, L) = q0

    • N.B. Duality!


    Viii long short run costs3
    VIII. Long- & Short-Run Costs

    • First, consider the production function

    • We envisage this as a collection of all efficient productiontechniques

    • Production Technique: Using particular combination of inputs (K, L) to produce output (q)

    • Consider the following:


    Viii long short run costs4
    VIII. Long- & Short-Run Costs

    • Assume firm has two production techniques (A, B) both of which exhibit CRS

    • Technique A requires 2 units of K and 1 unit of L to produce 1 unit of q

    • Technique B requires 1 unit of K and 2 units of L to produce 1 unit of q;


    Figure 18: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    Production Technique A (CRS)

    1q

    2K

    L

    0

    1L2L


    Figure 19: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    Production Technique A (CRS)

    fb (1K, 2L)

    1q

    2K

    2q

    Production Technique B (CRS)

    1K

    1q

    L

    0

    1L2L 4L


    Viii long short run costs5
    VIII. Long- & Short-Run Costs

    • We assume that firm can combine the two techniques

    • For example, produce 1 unit of q via Production Technique A and 1 unit of q via Production Technique B


    Figure 20: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    2q

    3K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    L

    0

    1L2L 3L 4L


    Figure 21: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    2q

    3K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    L

    0

    1L2L 3L 4L


    Viii long short run costs6
    VIII. Long- & Short-Run Costs

    • By combining techniques A and B in this way, the firm has effectively created a third technique

    • i.e. Technique ‘AB’

    • Technique AB requires 1.5 unit of K and 1.5 unit of L to produce 1 unit of q


    Figure 22: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    fab (1K, 1L)

    2q

    3K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    L

    0

    1L2L 3L 4L


    Figure 22: Production Techniques

    K

    fa (2K, 1L)

    2q

    4K

    fab (1K, 1L)

    2q

    3K

    fb (1K, 2L)

    1q

    4/3q

    2K

    2q

    2/3q

    1K

    1q

    L

    0

    1L2L 3L 4L


    Viii long short run costs7
    VIII. Long- & Short-Run Costs

    • If the firm is able to combine the two production techniques in any proportion, then it will be able to produce 2 units of q (or indeed, any level of q) by any combination of K and L

    • We can thus begin to derive the firm’s isoquont map

    • Isoquont: Line depicting combinations of K and L that yield the same level of q


    Figure 23: Production Techniques

    Isoquont Map (i)

    K

    fa (2K, 1L)

    2q

    4K

    2q

    3.5K

    1.5q

    3K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    0.5K

    0.5q

    L

    0

    1L 1.5L2L 3L 4L


    Figure 23: Production Techniques

    Isoquont Map (ii)

    K

    fa (2K, 1L)

    2q

    4K

    2q

    3.5K

    1.5q

    3K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    0.5K

    0.5q

    L

    0

    1L 1.5L2L 3L 4L


    Figure 24: Production Techniques

    Isoquont Map (iii)

    K

    fa (2K, 1L)

    2q

    4K

    fb (1K, 2L)

    1q

    2K

    2q

    1K

    1q

    L

    0

    1L2L 4L


    Figure 25: Production Techniques

    Isoquont Map (iv)

    K

    fa (2K, 1L)

    2q

    4K

    fb (1K, 2L)

    1q

    2K

    2q

    2q

    1q

    1K

    1q

    L

    0

    1L 2L 4L


    Figure 26 Production Techniques

    Isoquont Map (v)

    K

    fa (2K, 1L)

    2q

    4K

    fb (1K, 2L)

    1q

    2K

    2q

    2q

    1q

    1K

    1q

    L

    0

    1L2L 4L


    Figure 27: Production Techniques

    Isoquont Map (vi)

    K

    2q

    1q

    L

    0


    Viii long short run costs8
    VIII. Long- & Short-Run Costs

    • Consider discovery of production technique C

    • Technique C also exhibits CRS

    • But Technique C requires more inputs than Technique AB to produce q

    • It is therefore technically inefficient and would not be adopted by a profit maximising firm


    Figure 28: Production Techniques

    K

    fa (2K, 1L)

    2q

    fc (1K, 1L)

    2q

    fb (1K, 2L)

    1q

    1q

    2q

    2q

    1q

    1q

    L

    0


    Viii long short run costs9
    VIII. Long- & Short-Run Costs

    • Only technically efficient production techniques (such as Technique D) would be adopted

    • Thus, the firm’s isoquont will never be concave towards the origin and will in general be convex


    Figure 29: Production Techniques

    K

    fa (2K, 1L)

    2q

    fd (1K, 1L)

    2q

    fb (1K, 2L)

    1q

    2q

    2q

    1q

    1q

    1q

    L

    0


    Figure 30: Production Techniques

    Isoquont Map (vii)

    K

    fa (2K, 1L)

    2q

    fd (1K, 1L)

    2q

    fb (1K, 2L)

    1q

    2q

    2q

    1q

    1q

    1q

    L

    0


    Figure 31: Production Techniques

    Isoquont Map (viii)

    K

    fa (2K, 1L)

    2q

    fd (1K, 1L)

    2q

    fb (1K, 2L)

    1q

    2q

    2q

    1q

    1q

    1q

    L

    0


    Figure 32: Production Techniques

    Isoquont Map (viv)

    K

    2q

    1q

    L

    0


    Viii long short run costs10
    VIII. Long- & Short-Run Costs

    • The more technically efficient techniques there are, each using K and L in different proportions, then the more kinks there will be in the isoquont and the more it will come to resemble a smooth curve, convex to the origin

    • Analogous to consumer’s indifference curve


    Figure 33: Production Techniques

    Isoquont Map (x)

    K

    q1

    q0

    L

    0


    Viii long short run costs11
    VIII. Long- & Short-Run Costs

    • We can measure the firms Returns to Scale in terms of isoquonts by moving along a ray from the origin

    • i.e. returns to scale implies that firm is in the long run and can change bothK and L inputs

    • Thus:


    Figure 34: Returns to Scale

    K

    A

    3K

    2K

    q3

    1K

    q2

    q1

    L

    0

    1L 2L 3L


    Viii long short run costs12
    VIII. Long- & Short-Run Costs

    • CRS: q2 = 2q1

      q3 = 3q1

    • IRS: q2 > 2q1

      q3 > 3q1

    • DRS: q2 < 2q1

      q3 < 3q1


    Viii long short run costs13
    VIII. Long- & Short-Run Costs

    • We can measure the firm’s Returns to a Factor (i.e. K) by moving along a horizontal line from the particular level of K being held fixed

    • Note that firm will always incur decreasing returns to a factor, irrespective of its returns to scale

    • In what follows, we have CRS but DRF - successively larger increases in L are required to yield proportionate increases in q


    Figure 35: Returns to a Factor

    K

    A

    C’

    3K

    A B C

    2K

    3q

    A’

    1K

    2q

    1q

    L

    0

    1L 2L 3L


    Viii long short run costs14
    VIII. Long- & Short-Run Costs

    • Analogous to consumer’s budget constraint, we can also derive the firm’s isocost curve

    • Isocost curve: line depicting equal cost expended on inputs

    • c = rK + wL

    • Firm’s optimal choice - tangency condition


    Viii long short run costs15
    VIII. Long- & Short-Run Costs

    • Recall - firm’s problem:

    • Max q = f(K, L) s.t c = wL + rK = c0

    • or:

    • Min c = wL + rK s.t q = f(K, L) = q0


    Figure 36: Optimal Input Decision

    K

    c1/r

    E1

    K1

    q1

    L

    0

    c1/w

    L1


    Viii long short run costs16
    VIII. Long- & Short-Run Costs

    • Consider SR / LR cost of producing q

    • SR cost (say, when K = K1) is higher than LR cost except for one particular level of q

    • In the following example, c1 is minimum cost of producing q1 in both SR and LR

    • Rationale? Given (r, w), K1 is optimum (i.e. cost-minimising) level of K with which to produce q1


    Figure 37: LRTC and SRTC

    K

    c2

    A

    c1

    c0

    E0 E1 E2

    K1

    q2

    q1

    q0

    L

    0


    Viii long short run costs17
    VIII. Long- & Short-Run Costs

    • Thus, for every level of q≠ q1, short-run costs exceed long-run costs

    • Assuming increasing returns and then decreasing returns to both scale and to a factor, it must be the case that the short-run total cost curve (for a particular level of K) lays above the long-run total cost curve except at one particular level of output

    • Thus:


    Figure 38: LRTC and SRTC

    c

    LTC

    STC(K*)

    E1

    q

    0

    q1


    Viii long short run costs18
    VIII. Long- & Short-Run Costs

    • Consider underlying marginal cost curves

    • At q1,slopes of the SRTC and LRTC curve are equalsuch that SRMC = LRMC

    • For all q < (>) q1, slope SRTC < (>) LRTC such that SRMC cuts LRMC from below and to the left of q1


    Viii long short run costs19
    VIII. Long- & Short-Run Costs

    • Now consider underling average cost curves

    • SRAC = LRAC at q1 whilst SRAC > LRAC for all q ≠ q1 such that SRAC and LRAC are tangent at q1

    • N.B. Tangency does not imply that SRAC is at a minimum at q1, only that SRAC will fall/rise more rapidly than LRAC as q expands/contracts (i.e. not implication that SRAC will rise in absolute terms)


    Figure 40: LRAC Envelopes the SRAC

    c

    LMC

    SMC1

    LAC

    SAC1

    q

    0

    q1


    Viii long short run costs20
    VIII. Long- & Short-Run Costs

    • Now consider change in fixed level of capital

    • Recall - each short-run total cost curve is drawn for a specific level of fixed capital

    • As fixed level of K rises, level of q at which SRTC = LRTC also rises


    Figure 37: LRTC and SRTC

    K

    A

    K1

    q1

    K0

    c0

    q0

    c1

    L

    0


    Viii long short run costs21
    VIII. Long- & Short-Run Costs

    • If both LRAC & SRAC are u-shaped, then it must be the case that the former is an envelope of the latter


    Figure 39: LRAC Envelopes the SRAC

    c

    SAC1

    LAC

    SAC2

    SAC3

    SAC4

    SAC5

    SAC6

    q

    0

    qmes


    Viii long short run costs22
    VIII. Long- & Short-Run Costs

    • Note the tangencies between the LRAC curve and the various SRAC curves

    • Implication - SRAC will fallandrise more rapidly than LRAC as q contracts or expands


    Figure 40: LRAC Envelopes the SRAC

    c

    SMC3

    LMC

    SMC1

    LAC

    SAC1

    SAC3

    SMC2

    SAC2

    q

    0

    q1 q2 = qmes q3


    Viv final comments
    VIV. Final Comments

    • We now turn our attention to the revenue side of the firm’s profit maximising decision

    • We need to understand how revenue changes as we change output

    • i.e. Marginal Revenue (MR)

    • And how MR is determined by market environment within which the firm operates


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